mathematics

Käte Fenchel

Käte Fenchel is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Käte Fenchel rather than just read about it. In short: Käte Fenchel née Käte Sperling (21 December 1905 – 19 December 1983) was a German-born Jewish mathematician, best known for her work on non-abelian groups. Life Käte was born in Berlin to a newspaper reporter and a bookkeeper, Rusza Sperling (1878–1948).

Key takeaways

Käte Fenchel belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Käte Fenchel to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Käte Fenchel from memory before moving on to harder problems.

Reference excerpt

Käte Fenchel née Käte Sperling (21 December 1905 – 19 December 1983) was a German-born Jewish mathematician, best known for her work on non-abelian groups.

Life Käte was born in Berlin to a newspaper reporter and a bookkeeper, Rusza Sperling (1878–1948). As a child, she quickly learned to read and write, faster than most children. She was allowed to skip several grade levels and was awarded scholarships to attend private school. She enrolled at the University of Berlin, but she found that she faced daunting obstacles there in the form of gender discrimination because she was pursuing studies in pure mathematics. She was encouraged to write a thesis, but she never obtained the doctorate. As a result, Käte pursued an alternative career in mathematics education. After graduation, she began working at a job teaching mathematics at a German high school from 1931 to 1933 when Adolf Hitler and the Nazis rose to power in Germany. Käte lost her job because she was a Jew, as did Werner Fenchel, another German-born Jewish mathematician, who was removed from his teaching position in Göttingen. The two mathematicians arrived in Copenhagen in November and married in December 1933. They were joined in December 1938 by Käte's mother, who was able to emigrate from Germany. In 1940, the couple's son was born. While in Denmark, she helped facilitate the escape of other German Jews facing persecution. However, in 1940, the Nazi forces invaded that country so the young family, with Käte's mother, left with thousands of other refugees for Sweden. After the Allied liberation of Denmark, the Fenchels returned to Copenhagen, where Käte worked as a part-time lecturer job at Aarhus University in Denmark, from 1965-1970. Fenchel died on 19 December 1983.

Selected works Fenchel authored several academic papers, and published the last of them at the age of 73.

Fenchel, Käte. "On a theorem of Frobenius." Mathematica Scandinavica 42.2 (1978): 243-250. Fenchel, Käte. "A note about groups of odd order." Mathematica Scandinavica 10 (1962): 182-188. Fenchel, Käte. "Relationships between the structure of a finite group and a special representation." Monthly notebooks for mathematics 66.5 (1962): 397-409. Fenchel, Käte. "Moderne Algebra, Erster Teil, 2. Auflage.(Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band XXXIII)." (1938): 48-50. Fenchel, Käte. "L'algèbre abstraite. (Actualités scientifiques et industrielles, 362 (Abstract algebra)." (1938): 55-55. Fenchel, Käte. "Gruppen von linearen Transformationen.(Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 4, Heft 2)." (Groups of Linear Transformations. (Results of Mathematics and its Borderlands, Vol. 4, Issue 2)). (1935): 116-117.

References

Bibliography E. Høyrup ``Käte Fenchel" in Women of Mathematics: A Bibliographic Sourcebook. L. Grinstein, P. Campbell, eds New York: Greenwood Press (1987): 30–32

External links "Kate Fenchel", Biographies of Women Mathematicians, Agnes Scott College This article incorporates material from Käte Fenchel on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.

Worked examples

Example 1 — a first encounter with Käte Fenchel

Start with the simplest possible case. Write down what Käte Fenchel claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Käte Fenchel before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Käte Fenchel ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Käte Fenchel

In research: Käte Fenchel appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Käte Fenchel in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Käte Fenchel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1905 births, 1983 deaths, 20th-century German mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Käte Fenchel outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Käte Fenchel in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Käte Fenchel means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Käte Fenchel out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Käte Fenchel in simple terms?

Käte Fenchel née Käte Sperling (21 December 1905 – 19 December 1983) was a German-born Jewish mathematician, best known for her work on non-abelian groups. Life Käte was born in Berlin to a newspaper reporter and a bookkeeper, Rusza Sperling (1878–1948).

Why does Käte Fenchel matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Käte Fenchel?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Käte Fenchel.